NMR Coupling Constants Based on the Bethe-Salpeter Equation in the GW Approximation.

Area of Science:

• Computational Chemistry
• Quantum Chemistry
• Spectroscopy

Background:

• The Green's function GW (GW) method and Bethe-Salpeter equation (BSE) are powerful tools for electronic structure calculations.
• Extending these methods to molecular response properties, such as nuclear magnetic resonance (NMR) indirect spin-spin coupling constants, is crucial for accurate chemical predictions.
• Existing methods face challenges in accurately describing heavy-element systems and complex molecular responses.

Purpose of the Study:

• To extend the Green's function GW (GW) method and Bethe-Salpeter equation (BSE) to calculate molecular response properties, specifically NMR indirect spin-spin coupling constants.
• To develop and validate both nonrelativistic and quasi-relativistic formalisms for studying a wide range of molecular systems, including those with heavy elements.
• To enhance the efficiency and accuracy of these calculations through approximations and computational strategies.

Main Methods:

• Implementation of a quasi-relativistic two-component formalism to include scalar-relativistic and spin-orbit effects for heavy-element systems.
• Application of the resolution of the identity approximation to maintain computational efficiency.
• Utilizing the contracted BSE (cBSE) method, which incorporates Kohn-Sham correlation kernel, to improve accuracy for NMR coupling constants.
• Combining the eigenvalue-only self-consistent variant (evGW) with specific functionals (BH&HLYP, CAM-QTP family).

Main Results:

• Demonstrated performance on molecules with thousands of basis functions using CPUs and GPUs.
• Identified the importance of significant Hartree-Fock exchange for accurate GW quasi-particle energies.
• Showcased improved accuracy for NMR coupling constants using the GW-cBSE method, especially when combined with evGW and specific functionals.
• Successfully calculated the Karplus curve for tin molecules, validating the methodology for extended systems.

Conclusions:

• The developed GW-BSE methodology provides an accurate and efficient approach for calculating molecular response properties, including NMR coupling constants.
• The inclusion of Kohn-Sham correlation via cBSE and the evGW variant significantly enhances the accuracy for NMR properties.
• The quasi-relativistic formalism enables reliable studies of heavy-element systems, expanding the applicability of GW-BSE methods.